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A projection method for the spectral solution of non‐homogeneous and incompressible Navier–Stokes equations
Author(s) -
Pierro Bastien Di,
Abid Malek
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3700
Subject(s) - solver , mathematics , compressibility , projection method , pressure correction method , navier–stokes equations , computational fluid dynamics , incompressible flow , projection (relational algebra) , spectral method , turbulence , convergence (economics) , computation , numerical stability , flow (mathematics) , mathematical analysis , numerical analysis , mathematical optimization , geometry , mechanics , algorithm , physics , dykstra's projection algorithm , economics , economic growth
SUMMARY This paper is devoted to the development of a parallel, spectral and second‐order time‐accurate method for solving the incompressible and variable density Navier–Stokes equations. The method is well suited for finite thickness density layers and is very efficient, especially for three‐dimensional computations. It is based on an exact projection technique. To enforce incompressibility, for a non‐homogeneous fluid, the pressure is computed using an iterative algorithm. A complete study of the convergence properties of this algorithm is done for different density variations. Numerical simulations showing, qualitatively, the capabilities of the developed Navier–Stokes solver for many realistic problems are presented. The numerical procedure is also validated quantitatively by reproducing growth rates from the linear instability theory in a three‐dimensional direct numerical simulation of an unstable, non‐homogeneous, flow configuration. It is also shown that, even in a turbulent flow, the spectral accuracy is recovered. Copyright © 2012 John Wiley & Sons, Ltd.